Question

2. Given the following historical returns, calculate the average return and the standard deviation: Year Return 14% 10% 15% 11%

Answer 1

Year	Return
1	14%
2	10%
3	15%
4	11%

Average return is calculated using the formula:

Average return = E[R] = (R₁+R₂+R₃+R₄)/4 = (14%+10%+15%+11%))/4 = 50%/4 = 12.5%

Variance of a sample with a sample size of 4 is calculated using the formula:

Variance of the sample = σ² = [(R₁-E[R])² + (R₂-E[R])² + (R₃-E[R])² + (R₄-E[R])²]/3 = [(14%-12.5%)²+(10%-12.5%)²+(15%-12.5%)²+(11%-12.5%)²]/3 = (0.000225+0.000625+0.000625+0.000225)/3 = 0.0017/3 = 0.000566666666666667

Now, standard deviation is square root of variance

Standard deviation of return = σ = 0.000566666666666667^1/2 = 0.0238047614284762 = 2.38047614284762%

Answer

Average return = 12.5%

Standard deviation = 2.38047614284762%